Math Problem Statement

x² - 1

Solution

The expression x21x^2 - 1 is another example of the difference of squares. It can be factored using the formula:

a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)

Here, x2x^2 is a2a^2 and 1 is b2b^2, where b=1b = 1. So, the expression factors as:

x21=(x1)(x+1)x^2 - 1 = (x - 1)(x + 1)

Would you like more details or have any questions?

Here are 5 related questions:

  1. How would you factor x24x^2 - 4?
  2. What are the solutions to the equation x21=0x^2 - 1 = 0?
  3. How does the difference of squares apply to x29x^2 - 9?
  4. What if the expression was x2+1x^2 + 1 instead? Can it be factored?
  5. How do you expand (x1)(x+1)(x - 1)(x + 1) to verify the factorization?

Tip: When dealing with a quadratic expression, always check if it can be factored using the difference of squares, especially when the constant term is a perfect square.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Difference of Squares

Formulas

Difference of squares formula: a^2 - b^2 = (a - b)(a + b)

Theorems

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Suitable Grade Level

Grades 7-9